> Each day a disk jockey would read a serial number aloud on the air, and if any listener was able to produce the matching dollar bill they would win $30,000. Michael reasoned that 100,000 one dollar bills was 100,000 opportunities to win the prize, giving him a statistical advantage. [...] They soon realized that it was impossible for two people to examine that much money in the allotted time
This doesn't seem possible. Surely someone who thought the way he did would have realised that you could sort the money in advance.
So, thinking about how you would run this contest, you've got three basic ways of generating a random serial number.
The first is literally generating a random serial number; the problem being, there is an infinitesimal chance the serial number you just generated is in the pocket of someone in your listening area.
The second is to choose a sibling serial number of a bill in your pocket -- change one of the last couple of digits. If you're lucky, the sibling bills will have been delivered to the same bank in the same area and still be in circulation. But there's still a pretty slim chance it's even possible.
The best way to ensure that your contest is actually winnable, that your target bill is in circulation would be to start the contest by taking all the bills from your collective pockets, at the studio, writing down the serial numbers, and then handing them to someone to go buy coffee for the studio across the street. Wait a week or two, and your target bills will have circulated through the area enough, but almost certainly be in the pockets of people who could tune in and listen, and not someone halfway across the country.
So enter the 100,000 $1 bills sitting in stacks in this dude's house. Not circulating. At first, this isn't a problem -- he took out the bills after the contest start, after all -- but as time goes on, and the studio repeats the process of tagging and releasing new bills in circulation to generate new numbers to call out, suddenly, there is no chance that any of these hundred-thousand bills you are laboriously checking will work.
I worked at a small company for a short period of time where we would run a "contest" on social media, but then our social media guy would just comb through the entries and find someone attractive, in the right demo, and very active on social media and just give them the prize as a way to generate more social media buzz.
Back when the mafia used to have their own lottery (aka "the numbers"), there were two ways to pick the winning number (usually between 1 and 100).
Option 1:
Use the last two digits of some commonly available public number that was, essentially, random or at least unpredictable and not controllable. A good example today would be the cents portion of the SP500 index.
Options 2:
Tally up which of the numbers had the least amount of money bet on it and then make that the number.
You can guess which of the two options the more nefarious organizations used.
Interesting related note: back in the first half of the 20th century, there used to be a game in the newspapers where you were presented with a grid of faces, each one being numbered. The goal was to pick the face that you though OTHER people would pick most often. In other words, if you picked the most popular face, you would win. This led to lots of "well which face do I think other people will think is most popular etc"
John Maynard Keynes used the game above as a proxy for the stock market with stocks being the faces e.g. you were trying to pick the stock you thought that everyone else would buy.
In a past life I worked at a marketing agency. When we'd run random drawings, I'd (properly) randomly select and provide a winner.
It happened more than once that the marketing side would come back and ask for a new winner because of a situation like us doing a drawing for a prize from an ISP, and the winner's email being "@competitorisp.net".
As far as I know (and I've got a reasonable basis for this), the clients never requested this or anything. It was purely our marketing guys not liking the optics of telling the client that a competitor's customer won.
And yeah, for some giveaways and stuff they'd take a list of people and trawl through their social media accounts to figure out who'd have the most impact.
Again, don't think the clients had requested this, it just made the job we're doing look better to show the client "Yeah this person won and look at all the social media buzz it created!" rather than "Yeah we gave it to someone that looks like a troll, has no media presence, and the only people that will probably hear about this are a few people in an IRC chatroom."
If it's not regulated (or small enough that the regulators won't notice), I'd assume any contest/etc like this is probably rigged. Marketing is, generally, an industry full of lies. The contests are no different.
I worked next desk to a bunch of social media marketers, and then dealt with some individual social media marketers later on. My entire experience makes me immediately distrust anything such a person says. The only thing you can trust is that they'll do the thing that creates most engagement.
> The best way to ensure that your contest is actually winnable
This is definitely not a requirement according to some business owners. No shortage of faux competitions used to generate email signups around, even from reputable companies.
Closely related to this is the now accepted business practice of creating fake product offers to simultaneously gauge interest and collect e-mail addresses - where the actual product doesn't exist and only, maybe, will be developed if the scam generates good enough result.
Bonus points for using this to generate evidence for VCs you're courting.
Even if they physically had the bill and ensured it was in circulation in the city, the chances that someone has it and is listening to that radio station is so small. The radio station had to know it was an unwinnable contest. Why anyone would think they could win the contest is beyond me!
I don't know enough about this particular contest -- and since it happened in 1984, I'm not going to attempt to find more information on the internet -- but typically the goal isn't to have an unwinnable contest, just to have it drag on long enough while drawing more and more people into listening.
At the start of the contest, you might have 0.1% of the people in your listening area tuning in for the reading of the serial number, and by the end, 1-5%, before dropping down to, say, 0.2-0.5% after the contest is over. Early on, there's a 1 in a 1000 chance of someone listening having the bill, more or less, so the contest won't end too early, but by the end, you are up to a 1-in-20 chance, so once it gets popular enough, it will end fast enough that people don't get too much into grumbling that your contest is rigged.
Meanwhile, the radio station probably didn't actually put up the $30,000 -- it was probably an advertiser who paid the radio station $40,000 out of their advertising budget to run the contest, or should I say, the Wonder Widget's daily drawing, brought to you by Wonder Widgets, your wonderful source of wonderful widgets. You repeat the advertiser's slogan three or four times as people are tuning in to the station to listen for the day's serial number, and three or four more times throughout the day reminding people to tune in at X o'clock.
There's no need for the contest to be rigged or unwinnable -- it's a bargain for everyone at half the price. The advertiser knows people are listening to their ads, the radio station is getting paid outright as well as getting a boost in their listeners (which gets them more money from other advertisers). And actually paying out the money, eventually, lets you go back to that same gold mine again and again.
I totally agree, you want a hard to win contest so more and more people tune in. But I think you want...need... a winner. The radio station and the advertiser want a picture in the newspaper with someone holding a $30,000 cheque, you want that person screaming on the radio when they win. You want interviews with that person talking about how they will spend their winnings. A contest without a winner would be a terrible thing for everyone involved, well I guess for the ad agency putting in $30,000, maybe they get their money back?
This all reminds me of the lengths I went to a few years ago. An admin assistant in my office was really into these contests. She would listen to all the various stations and call in. There was a contest that was "identify this song" and everyday it went unguessed, they would add to the pot. It was getting up to $20,000 or something and no one could guess. I ended up downloading the clip and putting it through various Shazam like programs trying to help identify it. Never did win, but it was exciting for a short time. If after 30 days, they had just said, no one wins, I would have been pretty erked.
One of the common regulations you often hear about is "no purchase necessary" - even for games where most player get a chance to win by purchasing a product, they still need to provide some other mechanism like mailing in a request.
n = 100_000
K = 2 # seconds
time_secs = K * n * log(n)
t = timedelta(seconds=time_secs)
t # datetime.timedelta(days=26, seconds=56185, microseconds=92994)
So around a month (at 24×7, so in reality more like 3 months) of time sorting if in a horrendous abuse of big O notation we assume that sorting the notes takes 2 * n * log(n) seconds.
I guess he could use a pigeonhole sort though - at constant factor of 10 seconds this gives 11 days 49600 seconds.
Bigger problem is that there are 11.7 B one dollar bills in circulation [1]. Even having that $100k sorted you still only stand 1: 117000 chance of winning.
But there is no downside (besides the time cost of the one-dollar-bill operation). If you don't win, you just put the money back to the bank.
What is interesting is that you could theoretically deposit (part of) the money into your account and then withdraw somewhere else, so change the odds slightly.
That searching is quite expensive, considering the odds (only one chance per day). Besides, there was also significant additional downside, which became obvious in this case: The risk of having a pile of cash in your house which could be stolen
Back when this contest was running bank savings accounts paid enough interest that there was a real loss of having all your money withdrawn. I'm not sure what year this was, so I can't look up the interest rate, but a couple thousand lost per month isn't an unreasonable estimate.
> a couple thousand lost per month isn't an unreasonable estimate.
This was the mid-to-late 80's... it wasn't THAT long ago. The majority of people reading this were alive back then. Yes interest rates were higher in the 80s and 90s, but not as high as you are insinuating. At this time (from my memory) you could expect about 1% per year in interest. Maybe upwards of 2% annual interest if you had a very generous deal with a bank, but even that is unlikely.
At 1% a year, his $100,000 is generating ~$83 per month in interest.
Granted he could do other things with his money to appreciate it. Which would increase his time value of money. But the opportunity cost of checking/savings account interest was pretty small.
Granted the guy was stupid to begin with for even thinking he could win this contest and for putting $100k in cash in his house in case... I don't know, someone broke in or something... wait, that's what happened.
I'd sort into 10 piles by first digit, and then sort each pile into ten piles by second digit. This would involve looking at each note twice, so at two seconds per note it would take 400000 seconds, or around 7 days of two people working 8 hours a day. The small piles would have 1000 notes in them, which is easy to check in a day.
> The small piles would have 1000 notes in them, which is easy to check in a day.
By the time you could even buy an 8-bit home computer for couple hundred dollars, store all the serial numbers on a floppy and simply search through them once per day
Most likely scenario, you never look sort through it again. Least likely scenario, you get $30,000 (probably like $280,000 in today's money) to dig through them all one more time.
This scheme was such a profound misunderstanding of probability. You have 100,000 of the billions of dollar bills in circulation, so what? And of course his faulty risk assessment bit him in the end from the liability of having $100,000 in cash lying around.
If he had invested the $110k in the stock market in 1984 he would have been a millionaire at the time of his death in 1999, but crazies and normal people never see that.
You don't need to fully sort it. You do a really, really partial radix sort and stop at step one or two, because you don't need a perfect sort, just to cut it down to a few hundred bills instead of a 100K.
You trade an O(bucket size) linear search for the (log n) in the O(n log n) (assuming you optimally sort), which in computer terms is usually a bad idea but in this case, a significant savings.
Maybe this synopsis is mistaken, and to make the game winnable, the actual contest was to be the first to bring in a bill containing a substring of digits, which sorting wouldn't help with.
This doesn't seem possible. Surely someone who thought the way he did would have realised that you could sort the money in advance.